Roberto Mancini has told Vincent Kompany he needs to "pay more attention" following his sending-off for a tackle on Jack Wilshere in Manchester City's 2-0 win Arsenal on Sunday.

Although the captain had the automatic three-game ban issued for a straight red card overturned on appeal by an independent Football Association commission, his manager is conscious that Kompany could cost the side his services if he does not temper his tackling.

In January last season Kompany was also sent off in an FA Cup tie with Manchester United in similar circumstances and Mancini said: "He's a defender. Sometime when the defender is under pressure he can do a bad tackle but he needs to pay more attention, because this has happened two times. We can have a problem if we have another situation like this. I spoke with Vinny and told him to have more attention on his tackles."

Mancini, whose side host Fulham on Saturday, does not believe this will dilute the effectiveness of Kompany's tackling. "No. I don't think this but there are some situations that he can go [off] because, like against Arsenal, sometimes the referee can do a mistake like the players," he said. "I told him to pay attention and that it is better you don't go sometimes. You wait and don't do a tackle. Probably he won't change his style but, if he has more attention in some situations, it is better."

Mancini also brushed aside any notion that he was relieved now that Pep Guardiola will become Bayern Munich manager next season. This followed speculation that Mancini's job might be under threat, especially with Ferran Soriano, the new chief executive, and the sporting director, Txiki Begiristain, having previously worked with Guardiola at Barcelona.

Mancini said: "I did not have any problem with this. I can understand if in three years [here] we won nothing but we win three trophies in three years. We will probably continue to win in the future. The problem would be for the other managers who have not won anything in the last three or four years.

"This doesn't change because Ferran is CEO here and Txiki is sporting director. It does not mean that they keep Guardiola. We are here, I am here for three years. We started to build this team, we work harder. I know the people who are in charge here, they are serious people.

"When you decide to be a manager you should know you can lose your job in any moment. If you don't do your job well, you can tell [this] after two or three years but I think we did well until now."

Mancini added that he had never spoken to Soriano and Begiristain regarding Guardiola.